Detective Lt. Jack Fitzpatrick, the commander of the Suffolk County Police Department’s homicide squad, said investigators believed the fire started in the home’s living room. The fire was believed to be accidental, said Christopher J. Mehrman, the chief fire marshal for the town of Brookhaven.

Ms. McCusker was found in the bedroom where the twins slept in the rear of the house. Lieutenant Fitzpatrick said one of the twins had been removed from a crib, and it appeared as if Ms. McCusker were trying to remove the other twin.

Ms. McCusker and her children were pronounced dead at Brookhaven Memorial Hospital Medical Center in East Patchogue.

The Suffolk County medical examiner will perform autopsies to determine the causes of death.

Aidan was in second grade at John S. Hobart Elementary School in Shirley, where in March he was honored as Citizen of the Month. His father, Joseph Tarbell, posted a picture on Facebook of his son holding his certificate, writing, “Way to go Aidan.”

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The fire left the front of the home, with its brick-and-shingle facade and small concrete stoop, badly charred. By Saturday afternoon, it had been cordoned off with yellow tape, and boarded up. A neighbor, Ruthann Krafve, who said Ms. McCusker worked from home for an insurance company, said she heard her tell Aidan to go to bed around 9 p.m. on Friday.

Barely an hour later, the house was ablaze. Ms. Krafve said two of her sons, one an emergency medical technician and the other a former firefighter, tried to enter the home, but were driven back by the smoke and heat.

“I first saw a glow, which appeared to be from the living room, and in the time it took for me to run across the street, there was a boom, and the whole house was engulfed,” said Ms. Krafve, whose family was to go pumpkin picking with Ms. McCusker and her children on Sunday.

George Flamme, 46, who lives across the street, said the fire quickly consumed the home.

“The flames were just coming out the front window, coming out the side of the house, the front door,” he said. “It went up in no time.” He added, “You heard pop, pop, pop when the windows started blowing out.”

Mr. Flamme said that Mr. Tarbell had been staying in a basement apartment at the home while his own home underwent renovations, but that he was not there at the time of the fire.

Mr. Flamme described Ms. McCusker as “one of the greatest people on earth.” He said she had been caring for his 9-year-old son for the last three weeks, while he was in the hospital. He had only returned home a day before.

“People need to know what a wonderful person she was,” Mr. Flamme said, his voice cracking. “People have to understand that this is real life. We’re living this.”

Angela Macropoulos contributed reporting from Shirley, N.Y.

A version of this article appears in print on October 13, 2013, on Page A18 of the New York edition with the headline: A Mother and Three Young Children Are Killed in a House Fire on Long Island. Order Reprints|Today's Paper|Subscribe